Some insight into characterizations of minimally nonideal matrices

Lehman (Polyhedral combinatorics 1 of DIMACS series in discrete math. and theoretical computer science, pp 101–105, 1990) described some conditions regular minimally nonideal (mni) matrices must satisfy. Although, there are few results on sufficient conditions for mni matrices. In most of these results, the covering polyhedron must have a unique fractional extreme point. This condition corresponds to ask the matrix to be the blocker of a near-ideal matrix, defined by the authors in a previous work (2006). In this paper we prove that, having the blocker of a near-ideal matrix, only a few very easy conditions have to be checked in order to decide if the matrix is regular mni. In doing so, we define the class of quasi mni matrices, containing regular mni matrices, and we find a generalization on the number of integer extreme points adjacent to the fractional extreme point in the covering polyhedron. We also give a relationship between the covering and stability number of regular mni matrices which allows to prove when a regular mni matrix can be a proper minor of a quasi mni. Partially supported by CONICET Grant PIP 2807/2000 (Argentina) and by CNPq/PROSUL Grant 490333/2004-4 (Brasil).     

Existence of the non-primitive Weierstrass gap sequences on curves of genus 8

We show that for any possible Weierstrass gap sequence L on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at P is L. Combining this with the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some pointed non-singular curve. *Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science. **Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science.     

二元外代数的Z_n-Galois覆盖代数的Hochschild(上)同调群

设Λ是特征不整除n的域k上的二元外代数,■是Λ的Zn-Galois覆盖代数.首先构造了■的极小投射双模分解,并由此清晰地计算了■的各阶Hochschild同调和上同调群的维数;并且在域的特征为零时,计算了■的循环同调群的维数.     

ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS

For the K-quasimeromorphic mappings, a precise fundamental inequality for the angular domain is established. From this, the Borel direction of the K-quasimeromorphic mappings of zero order is derived.     

GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1：5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10^-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.     

粗糙表面分维计算的立方体覆盖法

针对三角形棱柱表面积法和投影覆盖法在计算粗糙表面分形维数中存在的问题,提出了计算粗糙表面分维的立方体覆盖法,对计算结果进行了对比分析,并进一步对表面分维计算中的有关理论问题进行了分析,发现立方体覆盖法作为一种几何意义上的覆盖法,并计算结果比三角形棱柱表面积法和投影覆盖法更接近实际。     

Strong Universal Pointwise Consistency of Recursive Regression Estimates

For semi-recursive and recursive kernel estimates of a regression of Y on X (d-dimensional random vector X, integrable real random variable Y), introduced by Devroye and Wagner and by Révész, respectively, strong universal pointwise consistency is shown, i.e. strong consistency P _X -almost everywhere for general distribution of (X, Y). Similar results are shown for the corresponding partitioning estimates.     

图的边覆盖染色中的分类问题(英文)

设 G是一个图 ,其边集是 E( G) ,E( G)的一个子集 S称为 G的一个边覆盖 ,若 G的每一点都是 S中一条边的端点 .G的一个 (正常 )边覆盖染色是对 G的边进行染色 ,使得每一色组都是 G的一个边覆盖 ,使 G有 (正常 )边覆盖染色所需最多颜色数 ,称为 G的边覆盖色数 ,用χ′c( G)表示 .已知的结果是对于任意简单图 G,都有 δ- 1≤ χ′c( G)≤ δ,δ是 G的最小度 .若 χ′c( G) =δ,则称 G是 CI类的 ;否则称为 CII类的 .本文主要研究了平面图及平衡的完全 r分图的分类问题     

Integral closure of a cubic extension and applications

In this paper, we compute the integral closure of a cubic extension over a Noetherian unique factorization domain. We also present some applications to triple coverings and to rank two reflexive sheaves over an algebraic variety.